Inhomogeneities in membranes give rise to localized interactions at the interface between domains in two-component vesicles. The corresponding energy is expressed as a line tension between the two phases. In this paper we study the implications of the thickness mismatch between domains which has been experimentally reported to be of order 20-30% and the conditions under which the induced line tension can destabilize the domains in inhomogeneous vesicles. For asymmetric lipidic membranes we prove an increase of the line tension and the existence of a contact angle. Adsorption of impurities is also examined, our scope being the extension of the Canham-Helfrich model to describe elastic deformations and chemical interactions arising at microscopic scales. This mismatch effect may have important consequences for the stability of very small domains.